Hermite representation for integrals?

[Mniazi]

Suppose I want an expectation value of a harmonic oscillator wavefunction, then in what way will I write the Hermite polynomial of nth degree into the integral? I have a link of the representation, but don't know what to do with them? http://dlmf.nist.gov/18.3

 

[dextercioby]

Why do you need the explicit form inside the integral? Leaving just H_n (x) is more than enough.

 

[Mniazi]

https://www.physicsforums.com/showthread.php?t=763320

 

[Jilang]

This gives you the first few...
http://www.bsu.edu/libraries/virtualpress/mathexchange/07-01/HermitePolynomials.pdf

 

[Mniazi]

ok If I have a integral like $$\int_{-\inf}^{\inf}{z*x*y}$$

then can I write them seperately as:

$$\int_{-\inf}^{\inf}{z}*\int_{-\inf}^{\inf}{x}*\int_{-\inf}^{\inf}{y}$$